Related papers: Set Contribution Functions for Quantitative Bipola…
Submodular setfunctions play an important role in potential theory, and a perhaps even more important role in combinatorial optimization. The analytic line of research goes back to the work of Choquet; the combinatorial, to the work of Rado…
We describe a new logical data model, called the concept-oriented model (COM). It uses mathematical functions as first-class constructs for data representation and data processing as opposed to using exclusively sets in conventional…
We augment Assumption Based Argumentation (ABA for short) with weighted argumentation. In a nutshell, we assign weights to arguments and then derive the weight of attacks between ABA arguments. We illustrate our proposal through running…
Recently, ranking-based semantics is proposed to rank-order arguments from the most acceptable to the weakest one(s), which provides a graded assessment to arguments. In general, the ranking on arguments is derived from the strength values…
Recently, it has been shown that many functions on sets can be represented by sum decompositions. These decompositons easily lend themselves to neural approximations, extending the applicability of neural nets to set-valued inputs---Deep…
We describe how answer-set programs can be used to declaratively specify counterfactual interventions on entities under classification, and reason about them. In particular, they can be used to define and compute responsibility scores as…
This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in…
The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. The special attention is given to modelling such functions by systems of functional…
In dialogical argumentation it is often assumed that the involved parties always correctly identify the intended statements posited by each other, realize all of the associated relations, conform to the three acceptability states (accepted,…
There is a growing interest in understanding arguments' strength in Quantitative Bipolar Argumentation Frameworks (QBAFs). Most existing studies focus on attribution-based methods that explain an argument's strength by assigning importance…
We present criteria for deciding whether a bivariate rational function in two variables can be written as a sum of two (q-)differences of bivariate rational functions. Using these criteria, we show how certain double sums can be evaluated,…
An extension of an abstract argumentation framework, called collective argumentation, is introduced in which the attack relation is defined directly among sets of arguments. The extension turns out to be suitable, in particular, for…
In this paper, we introduce the concept of the $\alpha$-fractal function and fractal approximation for a set-valued continuous map defined on a closed and bounded interval of real numbers. Also, we study some properties of such fractal…
In this paper, we compose a new task for deep argumentative structure analysis that goes beyond shallow discourse structure analysis. The idea is that argumentative relations can reasonably be represented with a small set of predefined…
Bipolar Argumentation Frameworks (BAFs) admit several interpretations of the support relation and diverging definitions of semantics. Recently, several classes of BAFs have been captured as instances of bipolar Assumption-Based…
Most publication and citation indicators are based on datasets with multi-authored publications and thus a change in counting method will often change the value of an indicator. Therefore it is important to know why a specific counting…
Elementary facts and observations on the cone of supermodular set functions are recalled. The manuscript deals with such operations with set functions which preserve supermodularity and the emphasis is put on those such operations which…
We demonstrate that statistics for several types of set partitions are described by generating functions which appear in the theory of integrable equations.
The theory of belief functions manages uncertainty and also proposes a set of combination rules to aggregate opinions of several sources. Some combination rules mix evidential information where sources are independent; other rules are…
The standard engineering approach to modelling of complex systems is highly compositional. In order to be able to understand (or to control) the behavior of a complex dynamical systems, it is often desirable, if not necessary, to view this…